Jan. 20, 1961
ACID-BASE EQUILIBRIA IN i%XTURES
ions inside the polyion or the effective charge is introduced. Therefore, the site-binding model, as proposed by Harris and Rice, may be the proper model for explaining the behavior of linear polyelectrolyte solutions.
[CONTRIBUTION FROM THE
OF
DEUTERIUM AND
PROTIUM
Acknowledgments,-I
OXIDES
305
wish to thank Professor
S. A. Rice and Dr. L. Kotin for their discussion and encouragement. I also wish to thank the National Science Foundation and National Institutes of Health for financial support, respectively.
DEPARTMENTS OF CHEMISTRY, CORNELL UNIVERSITY, ITHACA, NEWPORK, AND HARPUR COLLEGE, ENDICOTT, NEWY O R E ]
Acid-Base Equilibria in Solvent Mixtures of Deuterium Oxide and Water” BY E. A. HALEVI,~~ F. A. LONGAND M. A. PAUL RECEIVED JUNE 9, 1960 The dependence of the relative ionization constant of a weak acid on the atom fraction n of deuterium in a mixed deuterium oxidewater solvent is treated from a general point of view, with particular consideration of medium effects caused by the change in solvent. Various limiting formulations for comparison with experiment can be derived from the general equations, depending on the particular simplifying assumptions that are made. The Gross-Butler formulation, characterized by a cubic term in the denominator, results from assuming monohydrated protons and deuterons and additionally ignoring all medium effects, i.e., neglecting free energies of transfer of the relevant species from one medium to another. A “linear” formulation (with a iirst order term in the denominator) results if one postulates non-specific solvation for the protons and deuterons and again neglects free energy of transfer. Finally a “medium effect” formulation can be derived by assuming that the entire effect is due to free energy of transfer, i.e., that exchange fractionation is negligible. Comparison of these limiting formulations with experimental data for both ionization constants and rate coefficients of acid catalyzed reactions reveals that quite respectable fits may be obtained with each of them. However, for reactions that have K H / K Dor kD/kn values close to unity the Gross-Butler formulation fits considerably less well than the other two. Since the most likely actual situation is some superposition of contributions from medium effects and exchange fractionation, it seems highly doubtful that acid-base studies in mixed solvents will permit unambiguous conclusions about the state of solvation of the protons. Furthermore, in view of the likelihood that medium effects are of consequence, it is doubtful whether rate studies in the mixed solvents will permit choices to be made among kinetic mechanisms, a conclusion which was recently also reached by Gold from a different line of reasoning.
The theory of the solvent isotope effect for waterdeuterium oxide mixtures which was developed some time ago by Gross, Butler and their coworkers2-I permits a prediction of the variation with solvent deuterium content both of ionization constants of weak acids and of rate coefficients of acid-catalyzed reactions which involve a preequilibrium proton transfer. Recently Purlees has re-examined and up-dated this theory, especially in its parametric aspects. He introduced the now firmly established value of K = 4.0 for the equilibrium HzO
+ D10 = 2 H D 0
(1)
and also arrived a t a new value of L = 11for a second needed equilibrium constant, that for the exchange reaction 2D30’
+ 3Hz0 = 2H30’ + 3Dz0
(2)
Purlee then utilized several sets of experimental data, both kinetic and equilibrium, to arrive a t relevant values for a function Q’(n) (see equation 3). To do this last he established best values for a pair of parameters] kz+H and k3+H, which enter in this function. However, Purlee also showed that the rule of the geometric meangwould have sufficed to establish these latter and that in this sense Q’(n) is really (1) (a) Work supported in part by a grant from the Atomic Energy Commission. (b) On leave from Israel Institute of Technology, Haifa, Israel (1959-1960). (2) P. Gross, H . Steiner and P. Krauss, Trans. Faraday SOC.,32, 877 (1936). (3) P. Gross and H. Wischler, ibid., Sa, 879 (1936). (4) P. Gross, H. Steiner and H. Suess, ibid., Sa, 883 (1936). (5) J. C. Hornel and J. A. V. Butler, J . Chcm. Soc., 1361 (1936). (6) W. J. C. Orr and J. A. V. Butler,
